Anosov flows and Liouville pairs in dimension three

Building upon the work of Mitsumatsu and Hozoori, we establish a complete homotopy correspondence between three-dimensional Anosov flows and certain pairs of contact forms that we call Anosov Liouville pairs.We show a similar correspondence between projectively Anosov flows and bicontact structures, extending the work of Mitsumatsu and Eliashberg-Thurston.As a consequence, every Anosov flow on a closed oriented three-manifold M gives rise to a Liouville structure on R M which is well-defined up to homotopy, and which only depends on the homotopy class of the Anosov flow.Our results also provide a new perspective on the classification problem of Anosov flows in dimension three.